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Monday, July 7, 2014

It seems to be a widely held belief that randomized control trials are preferable if one is interested in determining causality. Causality is something of a slippery concept, but let us use the following definition: Drug A causes an increase in survival if drug A increases survival for at least ONE person relative to drug B.

I think this is a minimal requirement. If it is not true that drug A increases survival for at least one person relative to drug B, then drug A certainly does not cause an increase in survival.

If we observe the proportion of patients who survive on drug A and the proportion of patients who survive on drug B, can we determine if drug A causes an increase in survival?

No. We don't have enough information.

If more patients who take drug A live longer than patients who take drug B, we cannot (without more information) determine why they lived longer and whether it had anything to do with drug A.

What is the minimum amount of information we would need to determine if drug A causes greater survival? The answer is somewhat technical, but there are two cases where we could make the determination.

The first case is where we observe patient survival for a representative group of patients who only had drug B available. For example, prior to 2004 stage III colon cancer patients received 5FU as adjuvant therapy as oxaliplatin had yet to be approved by the FDA.

The second case is where we are willing to assume that patients are assigned to the drug for which their survival probability is higher. This is what is called a "behavioral" assumption. Such assumptions are relatively common in economics, but generally frowned upon outside of economics.

In both of these cases it is possible to determine whether drug A causes greater survival relative to drug B by simply looking at the probability of survival between those patients that take drug A and those patients that take drug B.

It is not necessary to have some ideal randomized control trial if we are able to observe survival for a group of representative patients who had no access to drug A or if we are willing to assume that patients are not assigned to the drug that is more likely to kill them.